GATE 2024 AE – Question 52

Structures · Strength of materials: Transformation of stress and strain, Mohr's circle, combined loading and failure criteria · 2 marks · Numerical answer

The state of stress at a point is caused by two separate loading cases. One of them produces a pure uniaxial tension along the $x'$ direction, and other one produces a pure uniaxial compression along the $y'$ direction, as shown in the figure. The sum of maximum and minimum principal stresses for the resultant state of stress caused by both loads acting simultaneously is ___________ N/mm$^2$ (rounded off to 1 decimal place).

Case I is a tension of 10 N/mm$^2$ along $x'$, and case II is a compression of 10 N/mm$^2$ along $y'$. The axes $x'$ and $y'$ are rotated $45^\circ$ from $x$ and $y$.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: -0.01 to 0.01

Explanation

In the $x'$-$y'$ axes the combined state is $\sigma_{x'} = +10$ and $\sigma_{y'} = -10$ with no shear, and these are the principal stresses. Their sum is the first stress invariant, $10 - 10 = 0$.